Transferring to Cal State Northridge in 1974 to be closer to the Hollywood studio scene, Geissman joined the Northridge "A" band led by jazz educator Joel Leach. While at Northridge, he began playing in both Gerald Wilson's Big Band and with Louie Bellson's Big Band, recording several albums with Bellson. For Louie Bellson's Live at the Concord Summer Festival, Geissman contributed an original composition, "Starship Concord." He began playing in local jazz joints with Tony Rizzi's guitar band, recording Tony Rizzi's Five Guitars Play Charlie Christian (1976), which featured Tom Ranier and Pete Christlieb.

Geissman's first gig with fluegelhornist/composer Chuck Mangione was at the Santa Monica Civic auditorium on November 9, 1976. A short tour of the Pacific Northwest followed, and soon after Mangione asked Geissman to become a permanent member of the band. Mangione's new band included Geissman, Charles Meeks on bass, Chris Vadala on woodwinds and James Bradley, Jr. on drums, and the first album with Mangione's new band was Feels So Good (1977), which sold two million albums and remains one of the top-selling instrumental albums today. On radio, the single "Feels So Good", featuring Geissman's now legendary guitar solo, was a huge international hit with many airplays, and a 1980 issue of Current Biography called it the most recognized tune since "Michelle" by The Beatles.

In 1978 Geissman released his first album as a leader, "Good Stuff" (Concord Jazz), which featured fellow Northridge alumnus Gordon Goodwin on sax, Tom Ranier on piano, Bob Magnussen on bass and Steve Shaeffer on drums. Grant left Mangione's band in 1981 to pursue other endeavors, including his own albums, session work and composing.

Geissman has released 13 albums as a leader. Two of his albums (Flying Colors and Time Will Tell) rose to the number one position in the Gavin and Radio and Records Contemporary Jazz airplay charts, and most of his recent recordings have cracked the top ten. He has recorded with such artists as Quincy Jones (Q's Jook Joint, 1995), Keiko Matsui, 3rd Force, David Benoit, Cheryl Bentyne, Lorraine Feather and Dianne Schur. He also had a guitar solo as a separate track on the Tiffany album Hold an Old Friend's Hand.

He was reunited with Mangione in 2000 when they recorded the album Everything for Love (Chesky Records). Geissman's early musical influences came full circle in 2003 when he played Dobro on Ringo Starr's Ringorama album. In 2006, he released his 13th album as a leader, Say That!, on his own label, Futurism Records. A throwback to the jazz music that first influenced him, he has described the sound of this album as "Wes Montgomery meets Horace Silver meets Jimmy Smith." John Kelman, in All About Jazz, reviewed:

It’s a shame that the words smooth jazz have become an oxymoron. Say That!, with its relaxed pace and easy-on-the-ears approach, is as smooth as it gets. But smooth jazz it ain’t. Geissman’s clear roots in the jazz mainstream, and a less-is-more style that reveals greater depth, makes Say That! a welcome return to the fold for a guitarist who’s always deserved more street cred than he’s received.

The Grant Geissman Quintet in 2006 included Brian Scanlon (woodwinds), Emilio Palame (piano), Kevin Axt (acoustic bass) and Ray Brinker (drums). After headlining the Playboy Summerfest at Pasadena's Rose Bowl, the Quintet followed with a debut at Yoshi's jazz club in Oakland, California and a performance in the Friday Night Jazz series at the Los Angeles County Museum of Art.

With Mangione, Geissman appeared on many of the major TV/variety shows of the time, including The Tonight Show, Dinah Shore, Merv Griffin, Phil Donahue, The Midnight Special, Don Kirshner's Rock Concert and Dick Clark's New Year's Rockin' Eve. Geissman's other albums with Mangione include Children of Sanchez (1978), Live at the Hollywood Bowl (1979) and Fun and Games (1980).

His playing has been heard on numerous TV shows, including Dawson's Creek, Family Affair, Boy Meets World, Touched By an Angel and Lizzie McGuire. He can be heard playing the Django acoustic guitar on the theme for the TV series Monk, starring Tony Shalhoub. Nominated for a 2001 Emmy for co-writing the song "No Puedo Olvidar" for the daytime drama Passions, he received an Emmy nomination in 2004 for another Passions song, "Momma, Gotta Let Her Go." In 2003, he was nominated for an Annie award for producing Van Dyke Parks' songs for HBO's Harold and the Purple Crayon. He has written additional music for films and TV movies, including The Ponder Heart (2001), Call Me Claus (2001), Monday Night Mayhem (2002), Die, Mommie, Die! (2003) and The Mojo Cafe (2004). Dennis C. Brown and Geissman collaborated on the underscore for the hit CBS-TV sitcom Two and a Half Men. The show’s theme, co-written by Geissman, was nominated for an Emmy Award in 2004.

Apart from his musical career, Geissman is an authority on Mad magazine and EC Comics and has written three books on the subject: Collectibly Mad (Kitchen Sink Press, 1995); Tales of Terror! The EC Comics Companion, co-authored with Fred von Bernewitz (Fantagraphics, 2000); and Foul Play! The Art and Artists of the Notorious 1950s E.C. Comics! (HarperDesign, 2005). He has also compiled and/or written annotations for ten other Mad-related books, and he appears in Chip Selby's documentary, Tales from the Crypt: From Comic Books to Television (2004).